Respuesta :
The required equation of the hypotenuse is 3x + 4y - 20 = 0
Solution:
Given, the points A(0,5), B(4,2), and C(0,2) form the vertices of a right triangle in the coordinate plane.
We are to find the equation of the line that forms the hypotenuse.
Assume the points in the co –ordinate plane, A and C are points on y – axis and B, C are points on a line perpendicular to y – axis. Which means AC and BC are legs of right angle triangle.
Thus, we note that the side AB is the hypotenuse of the triangle ABC.
Slope of a line passing through the points (a, b) and (c, d) is given by:
[tex]m=\frac{d-b}{c-a}[/tex]
[tex]\text { So, the slope of } \mathrm{AB} \text { is } \mathrm{m}=\frac{2-5}{4-0}=\frac{-3}{4}[/tex]
Since the line AB passes through the point A(0, 5), so its equation in point slope form will be
[tex]\begin{array}{l}{y-y_{1}=m\left(x-x_{1}\right)} \\\\ {y-5=\frac{-3}{4}(x-0)} \\\\ {4(y-5)=-3 x}\end{array}[/tex]
On rearranging terms to get standard form of equation,
3x + 4y -20 = 0
Hence, the required equation of the hypotenuse is found
